You apparently have an uncontracted Lorentz index b instead of index a in
je, which gives incorrect pairing of momenta when squaring the matrix
element. Propagator of W^- gives you a metric tensor ~ g[a, b]/(q^2-M_W^2)
and at low q gives ~ g[a, b] Gf

> Dear all,
>
> I am calculating a simple diagram and the program is returning the wrong
> answer.
>
> I have looked up my code thousand times and I don't think it has an error
> (plus I run the EWMuonDecayTree example and it gave me the same wrong
> answer....)
>
> Is this a bug or am I missing something very trivial?
>
> The proble is the following:
>
> I am calculating the muon decay matrix element, using the following code:
>
> (* Beging of the code *)
>
>
> (*This is Gf/Sqrt[2]Overscript[u, _](p3)\[Gamma]^a(1-\[Gamma]^5)u(p1)
> (muon curent) *)
>
> j\[Mu] = Gf/Sqrt[2]*Spinor[p3, 0].GA[a].(1 - GA[5]).Spinor[p1, m\[Mu]];
>
>
> (*This is Gf/Sqrt[2]Overscript[u, _](p4)\[Gamma]^a(1-\[Gamma]^5)v(p2)
> (electron curent) *)
>
> je = Gf/Sqrt[2] Spinor[p4, me].GA[b].(1 - GA[5]).Spinor[-p2, 0];
>
>
> (*This is to contract the \[Gamma] matrices*)
>
> M = (j\[Mu] MT[a, b] je // Contract);
>
>
> (* Matrix element <|M|^2>. Should be 64 Gf^2 (p1.p2)(p3.p4), see e.g.
> Griffths *)
>
> FermionSpinSum[M*ComplexConjugate[M]] /. DiracTrace -> TR
>
>
> (*End of the code *)
>
>
> The result it is giving is: 64 Gf^2 (p1.p3)(p2.p4) and not the well known
> 64 Gf^2 (p1.p2)(p3.p4).
>
>
> Now, if I run the EWMuonDecayTree example, it will show in the last line
>
> Check with the Okun, Chapter 3.2:CORRECT.
>
> But only because it is checking the final total decay rate and not the
> intermediate step (by lucky, it gave the correct result). If you run the
> EWMuonDecayTree, in the third output, after the Feynman Diagram, you will
> find the equivalent expression. Notice that the program gives ~(k.q1)(p.q2)
> which should be ~(k.q2)(p.q1)
>
>
> I am currently using version 9.2.0 and I also tested it on 8.2.0 and it
> gave the same results.
>
> Is there something wrong with my code and the example?
>
>
> thanks
>
>